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Quantum Consciousness

| Clifford Math of Consciousness at the Edge of Chaos |

| Superposition Separation | Structures | OrchOR | TimeScales - Table - Graph |

| Cycles: Biology and Quantum |

| Conscious Universe | Quantum Mind 2003 | QuanCon |


Clifford Math of Consciousness

The Discrete HyperDiamond Generalized Feynman Checkerboard and Continuous Manifolds are related by Quantum Superposition:


Dimi Chakalov said: "...

1. It is Heisenberg's uncertainty principle which Roger Penrose applied to collapse of the wave function, something like the instability and decay of a radioactive particle.

2. The picture is spacetime geometry separating from itself, and re-anealing after time T.

3. The greater the superposition, the faster the conscious event.

4. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs and one or the other is chosen. Thus consciousness may involve self-perturbations of space-time geometry.

5. Because OR phenomena are fundamentally non-local, the coherent superposition phase may exhibit puzzling bidirectional time flow prior to self-collapse.

6. You need collapse. Otherwise you're forever in pre-conscious superposition. ..." .

My thoughts are:

It looks to me as though "re-annealing" (in 2) = "collapse" (in 5 and 6).

In the Many-Worlds picture of the Multiverse Macrospace, you don't have collapse, but what happens is that you cease to experience ALL AT ONCE many superposed possibilities and you begin to experience EACH possibility IN ITS OWN "world" with no (or very limited) connections among the different "worlds".

If you think of an "apple per se", that must correspond to a particular geometric configuration of the tubulins in your brain. That configuration must be inter-related to other configurations in your brain (such as connecting the configuration for "Newton" to the configuration for "gravity" and then to the configuration for "Penrose", which would be a "stream of consciousness" for you), forming a "super-geometry of inter-relationships among configurations".

Now, I may also have a geometric configuration for "apple per se", and I may also have a "super-geometry of inter-relationships among configurations".

When we talk to each other about an "apple per se" are our geometric configurations for "apple per se" isomorphic, or is it the "super-geometry" that determines "apple per se" ?

What about using homomorphism of "super-geometry" instead of isomorphism, since you may have connections of "apple per se" to ideas that I do not have, and vice versa?

Maybe conversation is each telling the other about "super-geometry connections" thereby establishing new connections, with new connections sometimes causing laughter as in jokes, sometimes triggering further new connections as in creative conversation.

How can you describe this concept of consciousness mathematically, given 10^18 tubulins in a human brain?

Robert Neil Boyd has suggested that Consciousness could be modeled by Clifford algebras.

How could Robert Neil Boyd's suggestion work?

Each geometric configuration would be one subset of the 10^18 tubulins, which can be described by one element of the Clifford algebra Cl(10^18).

Clifford algebra can also describe a super-geometry of inter-relationships, since the Clifford algebra product combines both inner product and outer product, with the inner product determining what two geometric configurations have in common, and the outer product determining which configurations are in the exterior-wedge-outer product span-expansion of two geometric configurations.

Can you practically work with something as big as Cl(10^18) ? Yes - by repeatedly using the theorem that

Cl(N+8) = Cl(N) x Cl(8)

where x = tensor product, to decompose Cl(10^18) into MANY copies of Cl(8).

Cl(8) not only gives you the D4-D5-E6-E7 physics model (which thus appears to be generated by thought if the above picture is correct), Cl(8) also is based on Octonions, which have reflexive mathematical structures that can be useful in describing (and perhaps the source of) self-referential recursion phenomena.

For example, denote the Octonion basis by {1,i,j,k,E,I,J,K}. You can make an 8-dimensional lattice with Octonion structure from those given basis elements in 7 different ways, making 7 different lattices. All of the 7 different lattices are E8 lattices, and the set of the 7 different E8 lattices is isomorphic to the set of imaginary Octonion basis elements {i,j,k,E,I,J,K} so that you can use each of the 7 different E8 lattices as basis elements to make 7 different "super-lattices", etc.

For another example, look at the subsets of the 7 imaginary basis elements {i,j,k,E,I,J,K}. There are 7 three-element subsets that obey the associative law, called the 7 associative triangles by Onar Aam:

{i,j,k}, {i,E,I}, {j,E,J}, {k,E,K}, {i,j,K}, {i,J,k}, {I,j,k}

and the set of 7 associative triangles is isomorphic to the set of imaginary Octonion basis elements {i,j,k,E,I,J,K}.

Also, you have isomorphisms between the 7 associative triangles and the 7 E8 lattices, etc., and all these structures may be both rich enough and manageable enough to produce a useful mathematical model of consciousness.


Clifford Algebras Cl(N) = Cl(8) x Cl(N-8) = Cl(8) x ... x Cl(8) x Cl(N mod8) can descibe the Geometry of the States of the N Tubulin Site Electrons, but you need more to see how the Quantum Potential Landscape is determined.

The Quantum Potential Landscape is determined by Kauffman's NKC Coevolving Boolean Networks at the Edge of Chaos.

The Quantum Consciousness Superposition of 2^N States of the N Tubulin Electrons

begins with Input States of Tubulin Electrons and

ends with Output States of Tubulin Electrons.

During the Time of Quantum Consciousness Superposition, the Input States Coevolve (in the sense of Kauffman Coevolution, which is equivalent to Jack Sarfatti's Back-Reaction Loops and Roger Penrose's Tilted Lightcone Loops) with the Output States.

To see how this Coevolution works, first look at a

Kauffman NK Boolean Network

(see Kauffamn's books At Home in the Universe (Oxford 1995) or The Origins of Order (Oxford 1993), from which the images and much material of this section is taken). It has N Tubulin Electrons, each with the Boolean value 1 or 0, and with each Tubulin Electron receiving input from K other Tubulin Electrons (Connectivity =K).

If a Kauffman NK Network has connectivity K = (N-1), then each Tubulin Electron receives input from K other Tubulin Electrons, so that a Kauffman N(N-1) Network corresponds to the Clifford Algebra Cl(N), where (roughly):

N = Number of Tubulin Electrons = dimension of Vector

2^N = Number of States in Superposition = dimension of Clifford algebra

sqrt(2^N) = Median Length of Cycle of States = dimension of Full Spinor

N / e = Number of State Cycle Basins of Attraction = dimension of Vector

The N(N-1) Network corresponds to a very rugged Quantum Potential Landscape, with many Basins of Attraction. There are many small Basins, and relatively few large Basins, but most Basins are unstable with respect to small perturbations. In fact, some minimal perturbation transiently reversing one binary element will move the Network from one Basin of Attraction to any of the other Basins of Attraction. Therefore, the N(N-1) Network can be called Random and Chaotic. If regarded as a Cellular Automaton Computing Machine, its Randomness could be described as that of a Maximally Compressed Computation Algorithm in the sense of Chaitin's Halting Probability Omega.

This type of random landscape with many local optima is typical of all relatively large values of K:

When you get down to K = 8, you get to the Edge of Chaos. You see that the Median State Cycle length = B^N (where B is about 1.4)

and the Number of State Cycle Attractors is proportional to N = dimension of Vector.


At K = 2 there is a Phase Transition and Order emerges, with no more Chaos. At K = 2, the Median State

Cycle length = sqrt(N) and the Number of State Cycle Attractors = sqrt(N).


The Coupling of NK Input States to NK Output States

acts at the Edge of Chaos.

During the Time of Quantum Consciousness Superposition, the Input States Coevolve (in the sense of Kauffman Coevolution, which is equivalent to Jack Sarfatti's Back-Reaction Loops and Roger Penrose's Tilted Lightcone Loops) with the Output States. The Input States of the Superposition and its Output States form a Coupled Input State-Output State System that is anlogous to Kauffman's 2-species Coupled Coevolutionary NKC Boolean Network, described by Kauffman in The Origins of Order (here, some terminology has been changed to match the terminology of Quantum Consciousness):

"... an NK landscape represents the fitness landscape of the Input States of the Superposition. ... In a coevolutionary system, we need to represent the fact that both the fitness and the fitness landscape of the Input States are a function of the Output States. ... In the context of the NK model, the natural way to couple landscapes is to assume that each Tubulin Electron in an Input State [is connected to] K other Input State Tubulin Electrons internally and [to] C Output State Tubulin Electrons ... It is also natural to assume symmetry. ... C Input State Tubulin Electrons ... are coupled to each Output State Tubulin Electron ...

... In general, such a coevolutionary process admits of two behaviors. Either the partners keep dancing or the coupled system attains a steady state at which the local optimum of each partner is consistent with the local optimum of all the other partners by the C coupling. Such a steady state is the analogue of a pure-strategy Nash equilibrium [A Nash equilibrium is a combination of actions by Tubulin Electrons such that, for each Tubulin Electron, granted that the Tubulin Electrons do not alter their own actions, its action is optimal.]... Simulations were carried out between Input-Output pairs of coevolving States, each modeled on an independent NK landscape. ... The first major result is that Nash equilibria are encountered. ... When K is greater than C, Nash equilibria are found rapidly. When K is less than C, Nash equilibria are still found, but the mean waiting time becomes very long. ... for a pair of species whch are coevolving, K = C is a crude dividing line between these two regimes. ...

... a coevolutionary dynamics might tune the parameters ... such that the Quantum Consciousness Coupled Input State-Output State System as a whole coadapts well. ... there is an optimum value of K at K = 8 to 10 which optimizes mean fitness. ...


... The optimal ruggedness of fitness landscapes K = 8 to 10 achieved by selective tunnelling ... by the adapting System of Input States and Output States corresponds to coevolving Systems which have achieved the poised transition regime between order and chaos, [the Edge of Chaos]. ... For values of K less than and including K = 8, no freezing of the System occurs ... Such Systems are in the chaotic regime. For K = 10, entire Systems freeze at Nash equilibria gradually [A Nash equilibrium is a combination of actions by Tubulin Electrons such that, for each Tubulin Electron, granted that the Tubulin Electrons do not alter their own actions, its action is optimal.] ... For K greater than 10, Systems freeze rapidly. Such Systems are well into the ordered regime. The optimal value of ruggedness of landscapes K = 8 to 10 occurs just at that value where freezing begins. Thus model Systems optimize coevolutionary fitness when frozen components are tenuously extending across the System, when the System is in the transition region between order and chaos, [the Edge of Chaos]. ...".

Why are 8, 9, and 10 the Optimal Number of Links in a Kauffman NKC Coevolving Network?

Consider the Clifford Algebra decomposition Cl(N) into a tensor product Cl(8) x ... x Cl(8) that describes the Geometry of the States of the N Tubulin Site Electrons.

If the N Tubulin Site Electrons are grouped into (N/8) Groups of 8 by that decomposition, then each Group of 8 is fully interconnected in that each element receives input from the other 7 Links.

Using those 7 Links for internal interconnection in each Group of 8 means that

of the Optimal Numbers 8, 9, or 10 of Links,

there remain 1, 2, or 3 Links to be used externally to receive input from different Groups of 8.


Effectively the (N/8) Groups of 8 form a Kauffman (N/8)KC Network with K=C taking the values 1, 2, or 3.


At K=1, each Group of 8 only receives input (shown in red, with black -- denoting (possibly multiple) outputs) from one other Group of 8.


The Number of State Cycle Attractors is exponential in (N/8), and the Median State Cycle length is proportional to sqrt(N/8). The Network falls apart into separate loops with tails, somewhat like 1-dimensional Integer Lattices. About ln(N/8) sqrt(N/8) of the Groups of 8 lie of loops. The number of loops is about ln(N/8) / e. The Network is structurally modular, and composed of separate, isolated subsystems. Its overall behavior is the product of the behaviors of the isolated subsystems.


At K=2, each Group of 8 receives input (shown in red, with black -- denoting (possibly multiple) outputs) from two other Groups of 8,


so that branching trees can form, including 2-dimensional planar sheets, somewhat like Eisenstein Integer Lattices of Complex Numbers. The Number of State Cycle Attractors is about sqrt(N/8), and the Median State Cycle length is also about sqrt(N/8). The distribution of State Cycle lengths is not Gaussian, but is skewed in that most K=2 Networks have short State Cycles, while a few have very long State Cycles. K=2 Networks are Orderly, in that:

The basic principle allowing K=2 Networks to be so orderly is that K=2 Networks develop a connected mesh or frozen core of Groups of 8 that forms walls of constancy which break the system into functionally isolated islands of unfrozen Groups of 8 cut off from influencing one another by the walls of frozen Groups of 8.


The boundary regime where the unfrozen region is just breaking into unfrozen islands is the Phase Transition between Order and Chaos.


At K=3, each Group of 8 receives input (shown in red, with black -- denoting (possibly multiple) outputs) from three other Groups of 8, so that 3-dimensional structures can form, somewhat like Diamond Lattices.


The Number of State Cycle Attractors is proportional to (N/8), and the Median State Cycle length is B^(N/8) where B = 1.2565. K= 3 (and greater) Networks are Chaotic, and nearby states diverge.


A similar Clifford Algebra decomposition and Kauffman Network structure appears in the Simplex Physics of the Universe at Very High Energies.


Quantum Consciousness is not the only biological phenomenon that acts at the Edge of Chaos.

| Immune System | Heart |

Gerald Edelman, in his books Neural Darwinism (Basic Books 1987) and The Remembered Present (Basic Books 1989) has described the Immune System as a Neural Network. Such a Neural Network could act at the Edge of Chaos, and could not only describe the Immune System, but could also describe simple Neural Network Learning. Edelman also proposes that Neural Networks could describe evolution, but Kauffman also proposes that evolution should be described by his Kauffman NK Networks. Although there is some overlap between Edelman's Neural Networks and Kauffman's NK Networks, I think that Kauffman's NK Networks may prove to be a better model for evolution.

With respect to Simple Brain Structures that (to me) seem to be describable by Neural Networks, Bill Ditto and his coworkers at the applied chaos laboratory (ACL) of Georgia Tech have studied the Hippocampus of the Brain, and have demonstrated that they can stimulate brain tissue effectively with electric fields. They plan to attempt control of chaos using such field stimulation. They also will investigate and evaluate which if any of the control of maintenance of chaos techniques they have developed actually reduce or terminate seizure activity. This will be done initially in in vivo rat brain preparations and hopefully will evolve into human studies.

The Fractal Nature of Ventricular Fibrillation was described in 1982 by Johan Nicolaas Herbschleb.

Bill Ditto and his coworkers at the applied chaos laboratory (ACL) of Georgia Tech have also studied Controlling Chaos in the Heart.

With respect to atrial fibrillation in human hearts, which can lead to severe discomfort and a variety of deadly secondary conditions such as strokes, in collaboration with Dr. Jonathan Langberg at Emory University Medical Center, Bill Ditto and his coworkers at the applied chaos laboratory (ACL) of Georgia Tech are implementing real time control of chaos, shown to be effective in rabbit hearts, in humans undergoing Atrial fibrillation (both chronic and induced). They hope to be able to at least achieve partial control of the atrium or upper chamber of human hearts and extend such control to completely convert the fibrillation into normal sinus rhythms. This research, while quite aggressive, is already showing promising preliminary results.

It has been a long-standing controversy whether heart tissue undergoing ventricular fibrillation (cardiac arrest) exhibits chaotic or random behavior. Through a series of experiments conducted on dogs undergoing ventricular fibrillation by the Applied Chaos Laboratory and the department of Medicine at the University of Alberta, strong proof now exists that such hearts exhibit chaos. Unstable periodic motions of the type which are consistent with chaotic behavior and amenable to chaos control were observed in this set of experiments. This analysis is the first study of its kind to search for unstable periodic orbits in biological preparations ... .

In their paper Spatiotemporal evolution of ventricular fibrillation, Witkowski, Leon, Penkoske, Giles, Spano, Ditto, and Winfree say: "... Sudden cardiac death is the leading cause of death in the industrialized world with the majority of such tragedies due to ventricular fibrillation. Ventricular fibrillation is a frenzied and irregular heart rhythm disturbance that quickly renders the heart incapable of sustaining life. Rotors, the source structures that immediately surround the core of rotating spiral waves, occur in a variety of systems that all share with the heart the functional properties of excitability and refractoriness. These reentrant waves, seen in numerical solutions of three-dimensional simplified models of cardiac tissue are believed to occur during ventricular tachycardias. The detection of such forms of reentry in fibrillating mammalian ventricles has been difficult. Here we show that in isolated perfused dog hearts, high spatial and temporal resolution optical transmembrane potential mapping can readily detect transiently erupting rotors during the early phase of ventricular fibrillation. This activity is characterized by a relatively high spatiotemporal cross correlation. During this early fibrillatory interval frequent wavefront collisions and wavebreak generation are also dominant features. Interestingly, this spatiotemporal pattern undergoes an evolution to a less highly spatially correlated mechanism devoid of the epicardial manifestations of rotors despite continued myocardial perfusion.

In The New England Journal of Medicine (June 18, 1998, Volume 338, Number 25), Gregory D. Curfman, M.D. writes: "... Sudden death following a sharp but seemingly inconsequential blow to the chest is a frightening occurrence known as "commotio cordis" or "concussion of the heart." ... The victims are usually young people who die unexpectedly after a blow to the chest that does not appear to be unusually forceful. ... mostly young people who were struck in the chest while playing baseball, softball, or hockey ... Death is immediate, and with few exceptions, resuscitation is not possible. .... ventricular fibrillation is the cause of most fatal cases of commotio cordis. The investigators developed an experimental model of commotio cordis in anesthetized juvenile pigs. ... The authors constructed a device that delivered controlled impacts to the chest, simulating the impact of a baseball thrown at moderate velocity. The impacts were gated to the electrocardiogram so they could be precisely timed to particular phases of the cardiac cycle. When the impacts were delivered within a narrow temporal window between 30 and 15 msec before the peak of the T wave, ventricular fibrillation was reproducibly induced. The vulnerable period of the cardiac cycle amounted to just over 1/100 of a second. Remarkably, ventricular fibrillation was immediate, occurring on the very next heartbeat. The arrhythmia was not produced by impacts at any other time during the cardiac cycle, although transient complete heart block was sometimes observed with impacts during the QRS complex. Occasionally, with impacts delivered just outside the 15-msec period of vulnerability, unsustained polymorphic ventricular tachycardia was seen. ...".

According to a 10 May 2003 AJC article by Bill Montgomery and Brenden Sager: "... A 13-year-old Fayette County boy died after he was hit in the chest by a baseball pitched during a youth league ball game. The boy ... was struck on the left side of his chest by a ball that may have disrupted his heart's rhythm ... Last May, a 7-year-old boy died in Cobb County when he was struck in the chest by a batted ball. ...[he]... died from being struck precisely over the heart at precisely the right time to trigger cardiac arrest. Only five to 10 deaths similar deaths are reported each year, said Dr. Mark Link, associate professor of medicine at Tufts New England Medical Center in Boston. ...".


To see what is a T wave, go to the Virtual Cath Lab.



What Size Brains can be Conscious?


It is interesting that, at the crossing point where Tgrw = T_N, which is roughly where the Human Brain is located, is also roughly where N is such that it is equally in touch with

the Mind of the Universe (through GRW)


the self-conscious self (through the self-contained orchestration process).


If the GRW process is considered to be an expression of the Mind of the Universe, then the GRW termination may allow

small-N things to be more tuned in to the Mind of the Universe at large,


large-N things would be more self-absorbed by the self-contained orchestration process.


What about brains LARGER than human brains?

It may be that the human brain is about as large as a brain can get if it is to function as a single Large Scale Abstract Thought Consciousness based on the Biology Cycle.

The 2-brain structure of Dolphin brains may be a way to expand brain capacity beyond the size of 10^11 Neurons.

Another way may be to link many brains into a parallel computer, such as The Matrix.



What about brains SMALLER than human brains?

Since a Tubulin brain must be about 1 per cent of the human brain size to have Large Scale Abstract Thought Consciousness, an animal capable of it must have a brain that is at least 1 per cent of the size of adult human brains, or about 1 per cent of 1,400 grams, or about 14 grams.

The above image (from Evolution of the Brain: Creation of the Self, by John Eccles (Routledge 1989)) shows mammal brains drawn on the same scale. From it, it appears that Cats have brains that are about (1/3)^3, or about 3 or 4 per cent, of the size of human brains, and that Cats, Macaques, and Chimpanzees are capable of Large Scale Abstract Thought Consciousness, while Rabbits and Opossum are not.

You might also consider at what point in embryonic development a human brain becomes capable of Large Scale Abstract Thought Consciousness. For instance, the size of the human brain at birth is about 380 grams, with very rapid growth for the first 3 years. It may be relevant that the earliest conscious memory I have is of a time when I was about 4 years old.


I do not think that Biology Cycle Abstract Thought Consciousness is the only thing that is important:




Quantum Error-Correcting Codes and Quantum Games

According to S. Bandyopadhyay in quant-ph/9910032: "... quantum error correcting codes ... can correct errors due to decoherence through the use of appropriate software ...".

According to Apoorva Patel in his paper Quantum Algorithms and the Genetic Code, quant-ph/0002037: "Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural ... explanation of why living organisms have 4 nucleotide bases and 20 amino acids. ... these numbers arise as solutions to an optimisation problem. Components of the DNA structure which implement Grover's algorithm are identified, and a physical scenario is presented for the execution of the quantum algorithm. ... This genetic information processing takes place at the molecular level, where quantum physics is indeed the dominant dynamics (classical physics effects appear as decoherence and are subdominant). It is reasonable to expect that if there was something to be gained from quantum computation, life would have taken advantage of that at this physical scale. For DNA replication, the quantum search algorithm provides a factor of two speed-up over classical search ... Quantum algorithms can provide a bigger advantage for more complicated processes involving many steps. ... During DNA replication, the intact strand of DNA acts as a template on which the growing strand is assembled. At each step, the base on the intact strand decides which one of the four possible bases can pair with it. This is exactly the yes/no query (also called the oracle) used in the database search algorithm. ... What matters is only the relative phase between pairing and non-pairing bases. During the pairing process, the bases come together in an initial scattering state, discover that there is a lower energy binding state available, and decay to that state releasing the extra energy as a quantum. ... the base-pairing takes place not with a single Hydrogen bond but with multiple Hydrogen bonds (two for A-T and A-U, and three for C-G) ... Multiple Hydrogen bonds are necessary for the mechanical stability of the helix. But they are also of different length, making it likelythat they form asynchronously. With a two-step deexcitation process during base-pairing, the geometric phase change ... [is] ... what is needed ... DNA replication is observed to occur at the rate of 1000 base-pairings/sec. ... DNA is accurately assembled, with an error rate of 10^(-7) per base pair, after the proof-reading exonuclease action. Proteins are assembled less accurately, with an error rate of 10^(-4) per amino acid ...".

Mershin, Nanopoulos, and Skoulakis, in quant-ph/0007088, say: "... treat the tubulin molecule as the fundamental computation unit (qubit) in a quantum-computational net work that consists of microtubules (MTs), networks of MTs and ultimately entire neurons and neural networks. ...". They say "... it has been shown [by D. L. Koruga, D. L. Ann. NY Acad. Sci. 466, 953-955 (1986)] that the particular geometrical arrangement (packing) of the tubulin protofilaments obeys an error-correcting mathematical code known as the K2(13, 2^6, 5) code ... the existence of a quantum-error correcting code is needed to protect the delicate coherent qubits from decoherence. This has been the major problem of quantum computers until the works of Shor and Steane have independently shown that such a code can be implemented ... We conjecture that the K-code apparent in the packing of the tubulin dimers and protofilaments is partially responsible for keeping coherence among the tubulin dimers. By simulating the brain as a quantum computer it seems we are capable of obtaining a more accurate picture than if we simulate the brain as a classical, digital computer. ...".

Sharf, Cory, Somaroo, Havel, and Zurek, in A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy, quant-ph/0004030, say: "... This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13 C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics. ...".

Quantum Error-Correcting Codes are useful in Quantum Games.



According to Apoorva Patel in his paper Quantum Algorithms and the Genetic Code, quant-ph/0002037: "... Enzymes are the objects which catalyse biochemical reactions. They are large complicated molecules, much larger than the reactants they help, made of several peptide chains. Their shapes play an important part in catalysis, and often they completely surround the reaction region. They do not bind to either the reactants or the products ... for example, enzymes can suck out the solvent molecules from in between the reactants ... It is proposed that enzymes play a crucial role in maintaining quantum coherence ... Enzymes provide a shielded environment where quantum coherence of the reactants is maintained. ... For instance, diamagnetic electrons do an extraordinarily good job of shielding the nuclear spins from the environment ... the coherence time observed in NMR is O(10) sec, much longer than the thermal environment relaxation time ( hbar / kT = O(10^(-14) ) sec) and the molecular collision time ( O(10^(-11)) sec ), and still neighbouring nuclear spins couple through the electron cloud. ... Enzymes are able to create superposed states of chemically distinct molecules. ... Enzymes are known to do cut-and-paste jobs ... (e.g. ... methylation, replacing H by CH3, which converts U to T). Given such transition matrix elements, quantum mechanics automatically produces a superposition state as the lowest energy equilibrium state. ... Delocalisation of electrons and protons over distances of the order of a few angstroms greatly helps in molecular bond formation. It is important to note that these distances are much bigger than the Compton wavelengths of the particles, yet delocalisation is common and maintains quantum coherence. ...".


Quantum Tunnelling across Communicating Junctions:

Since the 1970s, Evan Harris Walker has proposed that Quantum Tunnelling of Electrons would take place across junctions between Neurons. Stuart Hameroff says in his Osaka paper that "... Gap junctions enable quantum tunneling among dendrites ...".

What is Quantum Tunnelling?

According to Principles of Modern Physics (McGraw-Hill 1959 at page 157) by Robert B. Leighton (who co-authored The Feynman Lectures in Physics),

if a particle such as an Electron encounters a Barrier such as the Synaptic Junction, "... there is a finite probability that the particle will ... be found on the other side ... This effect is also called ... the Tunnel Effect ... ".

From the point of view of Bohm Quantum Theory, Peter R. Holland (The Quantum Theory of Motion (Cambridge 1993) pages 198-203) says that Quantum Tunnelling is explained because the effective barrier potential is not the classical barrier potential V, but is V + Q where Q is the Bohm Quantum Potential.

From the Many-Worlds point of view, Quantum Tunnelling means that the Electron is in a Superposition of Position States, some of which are on one side of the Junction and some of which are on the other side.


Quantum Tunnelling can allow Quantum Superpostion States to extend from Neuron to Neuron across Gap Junctions.


Since a single Electron can move across 60-base chunks of DNA 20 nanometres long, Quantum Tunnelling for at least such distances could occur in DNA.


A process related to Quantum Tunnelling that might be useful in extending the coherent state of Tubulin Electrons throughout the Brain is "... the quantum mirage ... a ring of cobalt atoms on a copper surface ... acts as a "quantum corral", reflecting the copper's surface electrons within the ring into a wave pattern ... When the IBM scientists placed an atom of magnetic cobalt at one point in the ring, a mirage appeared at another point. ...",

according to a BBC article dated 8 February 2000, describing the work of Manoharan, Lutz, and Eigler in Nature, 403 (3 February 2000) 512-515, where they say: "... Image projection relies on classical wave mechanics and the use of natural or engineered structures such as lenses or resonant cavities. Well-known examples include the bending of light to create mirages in the atmosphere, and the focusing of sound by whispering galleries. ... Here we report the projection of the electronic structure surrounding a magnetic Co atom to a remote location on the surface of a Cu crystal; electron partial waves scattered from the real Co atom are coherently refocused to form a spectral image or 'quantum mirage'. The focusing device is an elliptical quantum corral, assembled on the Cu surface. The corral acts as a quantum mechanical resonator, while the two-dimensional Cu surface-state electrons form the projection medium. When placed on the surface, Co atoms display a distinctive spectroscopic signature, known as the many-particle Kondo resonance, which arises from their magnetic moment. By positioning a Co atom at one focus of the ellipse, we detect a strong Kondo signature not only at the atom, but also at the empty focus. This behaviour contrasts with the usual spatially-decreasing response of an electron gas to a localized perturbation. ...".

 Intercellular Light Communication

According to an article by Bennett Davis in the 23 Feb 2002 edition of The New Scientist:

"... In the early 1990s, Guenter Albrecht-Buehler ... at Northwestern ... discovered that some cells can detect and respond to light from others. ... cells ... were using light to signal their orientation. If so, they must have some kind of eye. ... centrioles fill the bill. These cylindrical structures have slanted "blades" which ... Albrecht-Buehler ... believes act as simple blinds. ... microtubules ... could act as optical fibres ... feeding light towards the centrioles from the cell's wall.

... why should cells want to detect light? ... they are talking to each other ... Cells in embryos might signal with photons so that they know how and where they fit into the developing body. ... Albrecht-Buehler ... wants to learn their language. ...

... In the 1980s Fritz-Albert Popp, then a lecturer at the University of Marburg in Germany, ... who now heads the International Institute of Biophysics in Neuss, Germany, ...[and]... runs a company called Biophotonen that offers its expertise in reading photon emissions to gauge the freshness and purity of food ... became interested in the optical behaviour of cells. In a series of experiments Popp found that two cells separated by an opaque barrier release biophotons in uncoordinated patterns. Remove the barrier and the cells soon begin releasing photons in synchrony. ...".



Entanglement/Coherence/Superposition Preservation in Solution:


Quantum Entanglement/Coherence/Superposition is what enables Quantum Computers to Work.

Chuang and Gershenfeld have shown that a Room Temperature Solution of Chloroform can function, by using NMR, as a Quantum Computer.

Caves has shown,using conventional physics, that because the Chloroform was at Room Temperature, its Atoms could not have been Entangled, and Quantum Computation should NOT have taken place.

However, NMR Quantum Computaton has been show to exist by using it to factor 15.

Perhaps NMR Quantum Computers live in a Quantum Protectorate.

Further, perhaps Unconventional Structures in Solutions (perhaps similar to water phenomena observed by Beneviste and to phenomena proposed by Mavromatos in quant-ph/0009089 based on "... conjectured (hydrated) ferroelectric properties of microtubular arrangements. ...[in which]... thin interior regions, full of ordered water, near the tubulin dimer walls of the microtubule. ... play the role of cavity regions, which are similar to electromagnetic cavities of quantum optics. ...[and in which]... the formation of (macroscopic) quantum coherent states of electric dipoles on the tubulin dimers may occur. ...".) could act to Preserve Entanglement/Cohererence/Superposition, thus permitting Quantum Computation,


Similar Unconventional Structures in Solutions could act in the Brain to Preserve Entanglement/Cohererence/Superposition,

even though the Brain is at body temperature.

It may be that the solution medium could act somewhat like the copper substrate in the IBM Quantum Mirage phenomenon


The 18 April 1998 issue of the New Scientist describes the Chuang-Gershenfeld quantum computer, saying:

"... In ... Physical Review Letters (vol 80, p 3408), the researchers describe how they used the nuclei of a carbon atom and a hydrogen atom in a chloroform molecule as two qubits. Both nuclei had spin 0 and spin 1 states, giving four combinations which existed simultaneously: 00, 01, 11 and 10. Using magnetic fields and radio waves, the researchers manipulated the atoms' spins, making them dance a nuclear jig corresponding to the algorithm's logic. The correct answer to the calculation came when a measurement of the spin states "snuffed out" those that did not match the target state. Chuang and his colleagues have since been working on other quantum algorithms, such as the "Deutsch-Jozsa" algorithm, which spots some properties of a mathematical function far faster than a classical computer. ...".

The abstract of Physical Review Letters (vol 80, p 3408) says:

"Using nuclear magnetic resonance techniques with a solution of chloroform molecules we implement Grover's search algorithm for a system with four states. By performing a tomographic reconstruction of the density matrix during the computation good agreement is seen between theory and experiment. This provides the first complete experimental demonstration of loading an initial state into a quantum computer, performing a computation requiring fewer steps than on a classical computer, and then reading out the final state."

The Chuang-Gershenfeld results are also discussed on a Physics Data-Mining web site and in a Scientific American (June 1998) article by Chuang and Gershenfeld.


There is an abstract of an article entitled Separability of Very Noisy Mixed states and Implications for NMR Quantum Computing, to appear in the 26 July 1999 issue of Phys Rev Lett, by S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, that states:

"We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable (unentangled). The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. The bounds show that no entanglement appears in the physical states at any stage of present NMR experiments. Though this result raises questions about NMR quantum computation, further analysis would be necessary to assess the power of the general unitary transformations, which are indeed implemented in these experiments, in their action on separable states.".

On page 20 of the 17 July 1999 issue of the New Scientist is an article by Charles Seife (a New Scientist Reporter) that says in part:

"... last April [1998], Isaac Chuang of IBM in San Jose, California, and Neil Gershenfeld the Massachusetts Institute of Technology created a quantum computer ... in a forthcoming issue of Physical Review Letters, Carlton Caves ... say they are unsure why quantum computation worked. Gershenfeld and Chuang used magnetic fields to manipulate atoms in liquid chloroform. But the problem, says Caves, is that the choloroform atoms were not in "entangled" states. ... because the chloroform was at room temperature, the atoms could not have been entangled ... The thermal motion of the atoms would have mixed up their quantum states and ruined any entanglement. ... So why did the chloroform comuter work at all? Caves's colleague John Smolin, a physicist at IBM in New York, suspects Chuang's chloroform has simulated a quantum computer, though he doesn't know how. Or maybe the experiment hints there are other ways of doing quantum computation that we don't yet understand. ...".


Vandersypen, Steffen, Breyta, Yannoni, Sherwood, and Chuang, in their paper Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance, quant-ph/0112176, say:

"... we report an implementation of the simplest instance of Shor's algorithm: factorization of N=15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule ...

.... as quantum bits, which can be manipulated with room temperature liquid state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to many quantum bit systems, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects in our system. ...".

Quantum Protectorate

( related to Meade Resonance )


According to cond-mat/0007287 by Philip W. Anderson:

"... Laughlin and Pines have introduced the term "Quantum protectorate" as a general descriptor of the fact that certain states of quantum many-body systems exhibit properties which are unaffected by imperfections, impurities and thermal fluctuations.

They instance the quantum Hall effect, which can be measured to 10^(-9) accuracy on samples with mean free paths comparable to the electron wavelength, and flux quantization in superconductors, equivalent to the Josephson frequency relation which again has mensuration accuracy and is independent of imperfections and scattering.

An even simpler example is the rigidity and dimensional stability of crystalline solids evinced by the STM.

... the source of quantum protection is a collective state of the quantum field involved such that the individual particles are sufficiently tightly coupled that elementary excitations no longer involve a few particles but are collective excitations of the whole system, and therefore, macroscopic behavior is mostly determined by overall conservation laws.

The purpose of this paper is, first, to present the overwhelming experimental evidence that the metallic states of the high Tc cuprate superconductors are a quantum protectorate; and second, to propose that this particular collective state involves the phenomenon of charge-spin separation, and to give indications as to why such a state should act like a quantum protectorate.

... Spin-charge separation is a very natural phenomenon in interacting Fermi systems from a symmetry point of view ... The Fermi liquid has an additional symmetry which is not contained in the underlying Hamiltonian, in that the two quasiparticles of opposite spins are exactly degenerate and have the same velocity at all points of the Fermi surface. This is symmetry SO(4) for the conserved currents at each Fermi surface point since we have 4 degenerate real Majorana Fermions. But the interaction terms do not have full SO(4) symmetry, since they change sign for improper rotations, so the true symmetry of the interacting Hamiltonian is SO4 / Z2 = SU2 x SU2, i.e., charge times spin. A finite kinetic energy supplies a field along the " direction of the charge SU(2) and reduces it to U(1), the conventional gauge symmetry of charged particles.

The reason why conventional Fermi liquid theory works is that U renormalizes to irrelevance because of the ultraviolet divergence of the ladder diagrams in 3 dimensions or higher. The result is the "effective range" theory which allows us to approximate the interaction terms, for forward scattering, by a scattering length a, which leads only to irrelevant symmetry-breaking terms.

In one dimension there is no ultraviolet divergence, this does not happen, and spin-charge separation always occurs. 2 is the critical dimension and I have shown that in fact there is always a marginally relevant term resulting from U, when there is spin symmetry. ...".


Acccording to cond-mat/0007185 by Philip W. Anderson:

"... The most striking fact about the high-Tc cuprates is that in none of the relevant regions of the phase diagram is there any evidence of the usual effects of phonon or impurity scattering. This is strong evidence that these states are in a "quantum protectorate" ... a state in which the many-body correlations are so strong that the dynamics can no longer be described in terms of individual particles, and therefore perturbations which scatter individual particles are not effective.

The Mott-Hubbard antiferromagnetic phase is manifestly spin-charge separated (there is a charge gap, but no spin gap), and I propose this property extends throughout the phase diagram in different guises, and is the reason for the quantum protectorate.

... scattering of electrons does not necessarily disturb the excitations, especially the spinons, the Fermion-like elementary magnetic excitations with spin 1/2 and charge 0.

... this protectorate effect is completely incompatible with any perturbative theory starting from a Fermi liquid approach, as for example the spin-fluctuation theory. The experimental situation presents us with a clean dichotomy, which cannot be repaired by "summing all the diagrams". ...

To summarize:

The two-dimensional electron gas in the cuprates is dominated by the short-range repulsive interaction which remains relevant and causes spin-charge separation.

A spin gap develops in the metallic phase below a crossover temperature T*, at the Cooper instability caused by the antiferromagnetic superexchange.

The extra kinetic energy required to open the spin gap is relaxed at a lower temperature Tc by making the charge fluctuations coherent, and this is the immediate cause of superconductivity. ...".


According to cond-mat/0301077 by M.Ya. Amusia, A.Z. Msezane, and V.R. Shaginyan:

"... the fermion condensation ... can be compared to the Bose-Einstein condensation. ... the appearance of ... fermion condensate (FC) ... is a quantum phase transition ... that separates the regions of normal and strongly correlated liquids. Beyond the fermion condensation point the quasiparticle system is divided into two subsystems, one containing normal quasiparticles, the other being occupied by fermion condensate localized at the Fermi level. ... fermion systems with FC have features of a "quantum protectorate" ... This behavior ...


Water, LightSpeed, and Microtubules

The interior of a Microtubule contains pure water that may be in an ordered state that might carry quantum-coherent oscillations (as sound or light waves). Such an ordered state of water has been observed to extend at least 3 nm outwards from cytoskeletal surfaces, so that it is not unreasonable to think that the ordered state could extend throughout the interior of a microtubule of interior diameter 14 nm.

If photons in Microtubule Cores have wavelengths that are of the order of a few times the inner diameter of Microtubles (about 14 nanometers), say, for example, about 100 nanometers, then the photons would have frequency about 3 x 10^10 cm/sec / 10^(-5) cm = 3 x 10^15 sec^(-1) which I think is ultraviolet and pretty energetic (at least 10,000 times more energy per photon than millimeter waves) for brain processes. However, it should be noted that Sonoluminescence can produce ultraviolet photons, so that maybe they could be involved in the Biology of Thought.

Rhett Savage says, about Water and Superradiance,
"...using quantum field theory, Del Giudice, Vitiello and others
wrote in the eighties that when an imposed electric field tries
to penetrate into a region of coherent or
at least polarized water
then it can do so only confined into filaments ...
outside of the filaments the original coherence
remains undisturbed.
Meanwhile, on the edges of the filaments there are weird
gradient forces which can attract or repel specific molecules
from the surrounding sea;
in this way ... the MTs are assembled.
Each time a molecule is drawn into the filament
by gradient forces then it alters the over-all wavefunction
so that the gradient forces chance everywhere
on the filament (nonlocally),
which changes which molecules are attracted and repelled ...
so these gradient forces are like Maxwell's demon
opening and shutting a door with great precision,
assembling the MTs and later serving as their
fundamental sense organ ...
...Del Giudice and friends went on to characterize
other aspects of the filaments.
they noted that a filament would undergo spontaneous symmetry
breakdown and develop Goldstone modes
and associated correlation -
then "the Coherence of the Goldstone correlation which
disappears because of the electromagnetic field propagation
is transferred to to the outgoing electromagnetic field." ...
... [this is] superradiance ...
Del Giudice and friends continue.
they say that the propagating of the resulting coherent
electromagnetic field undergoes a "self-focusing mechanism,"
allowing the field to propagate along the filament...
and, to top it all off, this mechanism is amplified because
the medium of ordered water within the filament is also coherent!
... [this is] self-induced transparency ...
the resulting picture is very cool: ..."
we start with an oriented polarization in water -
an electromagnetic field is applied,
cracks form in the polarization spontaneously:
these are the filaments that will be tubes.
they self-assemble the tubes from the ambient molecular sea
by a nonlocal Maxwell demon process.
then the tubes eventually serve as the guiding framework
for neurons, etc. - "

Self-Induced Transparency seems to be related to the Quantum Zeno and Anti-Zeno Effects.

Self-Induced Transparency has been used with laser beams passing through a Bose-Einstein condensate (BEC) of sodium atoms to increase the Refractive Index and slow the Speed of Light to 17 meters/second in a Harvard experiment reported by Lene Vestergaaard Hau et al (Nature, 18 February 1999), according to AIP Physics News Update 415 (18 Feb 99). They "... also observed unprecedentedly large intensity-dependent light transmission. Such an extreme nonlinear effect can perhaps be used in a number of opto-electronic components (switches, memory, delay lines) and in converting light from one wavelength to another.".

Mavromatos, in quant-ph/0009089, proposed a model based on "... conjectured (hydrated) ferroelectric properties of microtubular arrangements. ...[in which]... thin interior regions, full of ordered water, near the tubulin dimer walls of the microtubule. ... play the role of cavity regions, which are similar to electromagnetic cavities of quantum optics. ...[and in which]... the formation of (macroscopic) quantum coherent states of electric dipoles on the tubulin dimers may occur. ...".


Cytoplasmic Gel States and Ordered Water: Possible Roles in Biological Quantum Coherence is an interesting paper by Stuart Hameroff.


Acting as

Cellular Automata,

microtubules could transmit and process complex information signals as waves of polarization states of tubulin dimers.

The microtubules might be considered to be a combination of the Quantum Smart Matter of Hogg and Chase at Xerox PARC and the Quantum Cellular Automata of Meyer .

The 5+8=13 Fibonacci-number Golden Mean structure of microtubules may be useful in such information signal transmission and processing.


If the computing operations of the human brain were based on neurons alone, there would be 10^11 neurons operating at 10^3 signals per second, for a total throughput of 10^14 operations per second.

If the computing operations of the human brain were based on tubulin dimers, there would be 10^4 dimers per neuron, or 10^15 dimers, and the operating speed would be 10^9 operations per second, for a total throughput of 10^24 operations per second.

If the computing operations of the human brain were based on neurons, they would operate as a classical computer.

If the computing operations of the human brain were based on tubulin dimers, they could operate at the quantum level of superpositions of dimer polarization states.

If the human brain is then viewed as a quantum computer, perhaps quantum superpositions could resolve the problem of how a brain capable of understanding and appreciating the beauty and truth of such things as mathematical structures, music, and art could be based on a finite computing machine.



Sometimes I go beyond the Natural Units in which c = G = h = 1

to use what we used to call in college

SuperNatural Units in which c = G = h = 1 = 2 = pi

(In other words I sometimes ignore factors like 2 and pi, etc., for simplicity.)

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